Realization of One Flip-Flop using Other Flip-Flop

Realization of One Flip–Flop using Other Flip–Flop

• It is possible to convert one flip–flop into another flip–flop with some additional gates or simply doing some extra connection. Let us see few conversions among flip–flops.

 

1. SR Flip–Flop to D Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.1.

K–map simplification & Logic diagram

 

2. SR Flip–Flop to JK Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.2.

K–map simplification & Logic diagram

 

3. SR Flip–Flop to T Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.3.

K–map simplification & Logic diagram

• If we apply clock pulses to the circuit, the circuit output will toggle from 0 to 1 and 1 to 0. Thus, we can build 1–bit counter using SR flip–flop by converting it to T flip–flop.

Example: 1

Prepare the truth table for the circuit of Fig. 5.6.7 and show that it acts as a T–type flip–flop.

Solution :

For SR flip–flop,

Q_{n+ 1} = S+  Q_n

        = S+ SQ_n                   (because R=)

       = S (1+Q_n) = S

We have,

    S = Q_n ⊕ T

Q_{n+ 1} = Qn ⊕ T 

=Tn + Qn

Characteristic equation of T flip–flop.

Looking at column 1 and column 5 of Table 5.6.4 we can conclude that when T = 0, the output does not change and when T = 1, the output toggles. Thus, the given circuit acts as a T flip–flop. This is another way of implementing T flip–flop using SR flip–flop.

 

4. JK Flip–Flop to T Flip–Flop

The excitation table for above conversion is as shown in Table 5.6.5.

Logic diagram &  K–map simplification

 

5. JK Flip–Flop to D Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.6.

K–map simplification & Logic diagram

 

6. D Flip–Flop to T Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.7.

K–map simplification & Logic diagram

Example: 2

Analyze the circuit and prove that it is equivalent to T flip–flop.

Solution :

To analyze the circuit means to derive the truth table for it.

We have,   D = Input ⊕ Q_n

In the above circuit, output does not change when input is 0 and it toggles when input is 1. This is the characteristics of T flip–flop. Hence, the given circuit is T flip–flop constructed using D flip–flop.

 

7. T Flip–Flop to D Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.9.

K–map simplification & Logic diagram

 

8. JK Flip–Flop to SR Flip–Flop

The excitation table for above conversion is as shown in Table 5.6.10.

K–map simplification & Logic diagram

9. D Flip–Flop to SR Flip–Flop

• The excitation table for above conversion is as shown in Table 5.6.11.

K–map simplification & Logic diagram

 

10. T Flip–Flop to SR Flip–Flop

• The excitation table for conversion of T FF into an SR FF is as shown in the table.

K–map simplification & Logic diagram

 

11. D Flip–Flop to JK Flip–Flop

• The excitation table for conversion of D flip–flop to JK flip–flop:

K–map simplification & Logic diagram

 

Review Questions

1. Convert JK flip–flop to D flip–flop.

2. Convert D flip–flop into T flip–flop.

3. Convert JK flip–flop to T flip–flop.

4. Convert a SR flip–flop into a D flip–flop.

5. Convert a T–FF into an S–R FF. Draw the circuit.

6. How will you convert a D flip–flop into JK flip–flop ?

7. Convert SR flip–flop into JK flip–flop.

8. Convert SR flip–flop into T flip–flop.

9. Convert T flip–flop into D flip–flop.

10. Convert JK flip–flop into SR flip–flop.

11. Convert D flip–flop into SR flip–flop.

12. Realize D flip flop using SR flip flop.